OF ARTS AND SCIENCES. 267 



Tlie second condition, that the decrease in intensity in passing 

 through a tube is inconsiderable, is abundantly proved by the experi- 

 ments of Biot and Regnault in water-pijjes. The third condition, 

 that the intensity of resonance varies directly with the intensity of 

 vibration of the air just outside of the resonator, seems not to be sus- 

 ceptible of experimental proof, excepting on the assumption of the 

 law of inverse squares. 



There seems, however, to be no cause for a^y considerable varia- 

 tion from this ratio : and if, upon trial, we find that die law does hold, 

 it is reasonable for us to conclude that the variation of resonance is 

 proportional to the intensity ; for it is extremely improbable that there 

 would be two errors which would exactly counterbalance each other. 



The resonators having been adjusted so as to resound with equal 

 intensity by comparing them two at a time on the interference appa- 

 ratus, it was only necessary to connect three resonators as described 

 above, so that the resultant wave should act on the air contained in the 

 tube which enters the ear. Keeping now the pair of resonators in a 

 constant position, and moving the single resonator and one arm of 

 the interference apparatus until the resultant sound is at its minimum 

 intensity, the relative distances should be V2: 1. 



Below are given several series of readings of the distance of the 

 single resonator from the source of sound. The first three columns are 

 the results of experiments made in front of the pipe, the pair of reso- 

 natoi's being placed at a distance of 142 cms. from the embouchure. 

 The resonators were lettered, for convenience, A, B, and C ; and the 

 three series of readings are the results of opposing successively A to B 

 and C, B to A and C, and C to A and B. In the last three columns 

 are given the results of similar measurements behind the pipe, the 

 embouchure being still taken as the source of sound, and the pair of 

 resonators being distant 177.5 cms. 



At the bottom of the table the means are compared with the calcu- 

 lated positions of the single resonator. 



The mean of the means of the first three columns is 100.3 cm; 

 which differs from the theoretical by only 0.3 cm. The mean of the 

 last three is 128.2, giving a difference from theory of 3.2 cm. 



An inspection of the following table shows us, that, assuming the 

 embouchure of the pipe as the source of sound, in front of the pipe 

 the law of inverse squares holds almost exactly true : behind the jjipe 

 there is a slight difference. Theoretical considerations of the way in 

 which the sound-waves are given off from a closed pipe would lead us 

 to expect an error of this kind. The error due to the experiments 



